Calculus of Variations and Geometric Measure Theory
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L. Martinazzi

Concentration-compactness phenomena in the higher order Liouville's equation

created by martinazz on 06 Feb 2009
modified on 17 Jul 2018


Published Paper

Inserted: 6 feb 2009
Last Updated: 17 jul 2018

Journal: J. Functional Anal.
Volume: 256
Pages: 3743-3771
Year: 2009

ArXiv: 0809.2172 PDF


We investigate different concentration-compactness phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in $R^{2m}$, then that of a closed manifold and, finally, the particular case of the sphere $S^{2m}$. In all cases we allow the sign of the Q-curvature to vary, and show that in the case of a closed manifold, contrary to the case of open domains in $R^{2m}$, concentration phenomena can occur only at points of positive Q-curvature. As a consequence, on a locally conformally flat manifold of non-positive Euler characteristic we always have compactness.


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